Here some responses from officials.
1. By rule, we have to grant a TO if it's requested while the ball is dead (before the snap). The timing of the whistle has no effect on if they get it or not. Officially the rule says "...an official shall allow a charged team timeout when requested by any player or head coach when the ball is dead"
If we're down near the goal line, we instruct the coach that they may run down the sideline to get our attention to request the TO (we're not looking back to the box).
2. Check Rule 3-4-3 (all parts). As Rob S said, if the ball is dead - and it is dead until it begins to move for a snap - a Head Coach or any of the 11 players on the field may request a timeout, and it SHALL be granted, if the ball is dead. An official may see the gesture or hear the verbal request a fraction of a second before the ball begins to move for the snap. At that instant, that official declares the ball dead in his mind, and checks the game clock for remaining time. It may take another half second to begin sounding his whistle, and begin signaling time out, while charging in toward the referee, to report the granted timeout and his positive knowledge of the time remaining. The clock will then be re-set as needed.
This isn’t interpreted. It is by rule. And the HC (only) may leave the team area for the exclusive and express purpose of requesting a timeout. So, yes, he may leave the team area, run down toward an official to get his attention and request a TO.
Hope this helps.
I am still trying to get better clarification of a coach actually being in the field of play while the players are in the process of lining up, or later.
As for the Calhoun situation. There was a lot more to his outcome than is public knowledge. Should a coach retain an upperclassman that has walked a fine line off the field, missed classes consistently, and didn't apply himself much academically? If so, what kind of example would that be setting for the younger players? Hauck made the right decision.